Can you tell us exactly what are you planning to use it for, what is the scenario?
It is possible to create Element Properties in the Property Manager, and the Property can return the Volume of the element it is assigned to (Wall, Slab, etc.). Is this what you are after?

I know I can use volume, but I was thinking about mass as a weight-measure. I know that 3D objects are empty, they do not contain "insides". But can I add some kind of parameter which will be read in IFC as weight/mass of the object for example.

Building materials have a value for 'Density kg/m³' which you can adjust.
This can be schedule but it s still not quite what you are after.
You can schedule the volumes and the density, but you can not multiply them to get the mass.

You would have to create a property object that could read the density value of each skin (building material) and then multiply it (expressions in properties) by the volume of that skin to give you the total mass.
I am not sure if this is possible as I have not tried it myself.
I am not sure if you can get the density value of a building material via properties.

If not you could add a total 'density' property to each wall and then use an expression to calculate a property for the 'density x volume' of the entire wall (rather than each skin).
You would have to manually add the correct density value to each wall You can create a default value in the properties that will be applied to all walls and can be altered for each wall) or create another expression in properties that could set the value base on the composite name of the wall - assuming you have a very regimented list of walls that you use and you don't just make them up as you go.